Details on ongoing research effort that looks into enhancements of the BADA model are provided. The work is undertaken in cooperation with Boeing Research ...
Paper presented at 24th Digital Avionics System Conference, Washington D.C. October 30 – November 3, 2005
ADVANCED AIRCRAFT PERFORMANCE MODELING FOR ATM: ENHANCEMENTS TO THE BADA MODEL Angela Nuic, Chantal Poinsot, Mihai-George Iagaru Eurocontrol Experimental Centre, Brétigny sur Orge, France Eduardo Gallo, Francisco A. Navarro, Carlos Querejeta Boeing Research & Technology Europe Madrid, Spain
Abstract An efficient Air Traffic Management (ATM) system requires planning of traffic flows that rely on accurate estimation of aircraft performances. New operational concepts, that will ensure seamless management of the forecasted growth of air traffic and provide increased capacity, are based on aircraft trajectory prediction. An aircraft performance model is the core of trajectory computation and therefore plays a central role in the development and evaluation of the future ATM systems. The Eurocontrol Experimental Centre conducts a number of activities in the domain of aircraft performance modeling, which are performed within the scope of Base of Aircraft Data (BADA). This paper briefly introduces BADA, its purpose, application and users. Then it focuses on the BADA model structure and addresses various aspects of aircraft performance modeling for ATM applications. Details on ongoing research effort that looks into enhancements of the BADA model are provided. The work is undertaken in cooperation with Boeing Research & Technology Europe (BR&TE). The advanced approach to aircraft performance modeling is based on exploiting today’s aircraft performance resources, data and software, that were not available in the past when BADA was initially developed. Encouraging results that demonstrate significant improvement in BADA aircraft performance model capabilities are presented in the paper.
on accurate estimation of aircraft performances. New operational concepts, that will ensure seamless management of the forecasted growth of air traffic and provide increased capacity, are based on aircraft trajectory computation. An aircraft performance model is the core of trajectory prediction and therefore plays a central role in the development and evaluation of the future ATM systems (see e.g. [1], [2] and [3]). There are several existing approaches to aircraft performance modeling to support various needs for aircraft trajectory prediction and simulation. Kinetic approaches model aircraft forces, while kinematic approaches directly model the path characteristics of the aircraft without attempting to model the underlying physics. Depending on the approach and techniques used in modeling there are different forms of Aircraft Performance Models (APM). Typical examples that are used today are introduced and described in [2]. Base of Aircraft Data (BADA) is an aircraft performance database based on the kinetic approach to aircraft performance modeling that has been developed and maintained by the Eurocontrol Experimental Centre (EEC). The information provided in BADA is designed for use in trajectory simulation and prediction in ATM research as well as for modeling and strategic planning in ground ATM operations. Historically, within the EEC, the accuracy of aircraft performance modeling was of significant importance to achieve realistic aircraft performances in a simulation environment.
Introduction
This paper focuses on research effort and the latest achievements in the domain of aircraft performance modeling undertaken by the EEC within the scope of BADA.
An efficient Air Traffic Management (ATM) system requires planning of traffic flows that rely
The paper is structured in three parts. In the first part, an overview of the BADA model
©2005 - The European Organisation for the Safety of Air Navigation (EUROCONTROL). All rights reserved. The content represents the Author’s own views which do not necessarily reflect EUROCONTROL’ official position
structure and aspects of the model identification process are given, followed by information on the state-of-the-art of the current BADA version. The second part is dedicated to the research work on the model enhancements. It describes approach and methodology and provides results of the BADA model improvement. Conclusions are summarized in the third part.
Motion Total Energy Model or TEM relates the geometrical, kinematic and kinetic aspects of the aircraft motion, allowing the aircraft performances and trajectory to be calculated. TEM equates the rate of work done by forces acting on the aircraft to the rate of increase in potential and kinetic energy, that is: .
BADA Model overview The APM adopted by BADA is based on a mass-varying, kinetic approach. This approach models an aircraft as a point and requires modeling of underlying forces that cause aircraft motion. The structure of BADA APM is represented in figure 1. Figure 1 Structure of BADA APM
APM
. T − D v ⋅ ESF h = mg
(2)
v dv where g is the gravity and ESF = 1 + g dh
−1
(3)
is the energy share factor.
.
m = −F
Aircraft Characteristics
Operations
where h is altitude, h is vertical speed, v is true airspeed (TAS) and m is aircraft mass. To facilitate calculations, equation (1) can be rearranged and vertical speed expressed as
The variation of mass is accounted for through the fuel consumption model:
Actions
(1)
.
Model Structure and Main Features
Motion
.
(T − D )v = W h + mv v
Limitations
As depicted in figure 1, the BADA APM is structured in 5 models, namely Actions, Motion, Operations, Limitations and Aircraft Characteristics. The dependencies among the models are represented with dashed arrows (which point towards the models that the one at the origin of the arrow depends upon). Actions This model allows computing the forces acting on the aircraft which cause its motion. There are three categories of actions: aerodynamic (namely drag D and lift L), propulsive (thrust T) and gravitational (weight W). Since BADA accounts for mass variation, the propulsive model provides an associated model to compute fuel consumption F.
(4)
Equations (2) and (4) together form an Ordinary Differential Equations (ODE) system which can be posed with the respective initial or boundary conditions at each flight segment to compute the aircraft motion in that interval. The computed aircraft trajectory is, then, the result of concatenating the solutions of a sequence of such motion problems. Operations Although the ODE system above governs any possible aircraft motion, different ways of operating the aircraft result in different trajectories. For instance, flying constant Mach number leads to the following specific form [4] of equation (3): −1
κRβ T (5) ESF = 1 + M 2 2 g where κ is the air adiabatic index, R is the specific gas constant, βT is the temperature gradient of the particular atmosphere layer considered, M is Mach number. Analogously, flying constant calibrated airspeed (CAS) leads to a different form of equation (3) and
so on for other flight regimes other than constant CAS/Mach. The Operations model is responsible for capturing those aspects (such as the ESF), which are neither directly related to actions nor motion laws, but which are necessary to incorporate into the problem of computing aircraft motion, the knowledge about the way in which the aircraft is operated. The Operations model is conceived to fill the gap between the Actions and Motion models. Thus, provided that the way of operating the aircraft is known (e.g. constant CAS), the Operations model provides the features that are needed to bring actions and motion together thereby closing the mathematical problem to compute the resulting aircraft trajectory –e.g. the model expressed in (5). Limitations Limitations restrict the aircraft behavior in order to keep it between certain limits to safeguard the safe operation of the aircraft, or limit the equipment degradation. The applicable limitations have been classified into four categories, namely geometrical, kinematic, dynamic and environmental. Geometrical limitations include the maximum certified altitude, maneuver limited altitude etc. Kinematic limitations refer to speed limitations such as maximum operating airspeed/Mach (VMO/MMO), low and high speed buffet, landing gear and flaps speed limits and the speeds that serve to define maneuver envelope. Dynamic limitations include throttle limits for standard ratings and aircraft weights such as the maximum takeoff weight (MTOW), maximum payload (MPL) etc. Finally, environmental limitations include stand for the environmental envelope. Aircraft Characteristics Each aircraft is described with a set of coefficients which represent characteristics used by the previous models, but that are intrinsic to the aircraft, such as the aerodynamic reference area, wing span, etc.
Model Instances for Specific Aircraft Once aircraft model components, structure and algorithms are defined, identification of a model instance for a specific aircraft type can take place.
This process specifies corresponding aircraft model parameters and coefficients aiming to achieve the best fit between calculated and reference aircraft performance data. Aircraft Performance Reference Data Aircraft type identification depends and heavily relies on availability, type and quality of aircraft performance reference data.
In the past, the main sources of aircraft performance reference data were Aircraft Operation Manuals (AOMs), published by aircraft manufacturers or operating airlines. From aircraft performance modeling perspective, AOMs provide valuable information on aircraft limitations, performances and operating procedures for all aircraft types that have ever been put in operation. Aircraft performances are given in form of integrated flight profiles that specify time, distance and fuel to climb/descent to/from specific flight level. Data is given for number of flight levels, with variable altitude step that sometimes results in low number of data points. Depending on source AOM, time to climb or decent is rounded to minute which inevitably reduces precision of the data. Due to the intended purpose of AOM, aircraft performance data for nominal aircraft operating speeds in climb, cruise and descent is only provided. Nowadays, aircraft manufacturers develop aircraft performance engineering programs that can provide a high quality aircraft performance reference data. These programs allow generation of reference data for complete range of aircraft operating conditions in terms of weight, speeds, ISA and associated operating regimes with high level of data granularity (number of data points) and data precision. Currently, such programs exist for limited number of aircraft types (e.g. INFLT/REPORT Boeing Performance Software, PEP Airbus Performance Engineering Program. However, it is to expect that, in the future, similar capabilities will be provided for all aircraft types. Existence of this type of data opens new horizons in the domain of aircraft performance modeling which is demonstrated in this paper. Aircraft Model Instance Identification BADA represents an aircraft as a point and requires modeling of the resulting longitudinal
forces affecting this point – thrust and drag, while fuel flow is modeled as a function of thrust. As the original aircraft data for thrust, drag and thrust specific fuel consumption was, and still is not easily available, a choice was made to use aircraft profile data for BADA aircraft model identification. The ODE system formed by equations (2) and (4), together with equation (6) below provides the way to compute flight profiles based on BADA, once the model coefficients for thrust, drag and fuel consumption are known. .
r = v ⋅ cos γ
(6)
.
where r is the horizontal speed and γ is the flight path angle. The objective of model identification process is to obtain the optimum coefficients from a set of known flight data points. Since the ODE system is the law that governs trajectory generation according to BADA model, it can be used for coefficient identification purposes (left side values of expressions (2), (4) & (6) are the observed values while right side values are the predicted values by means of the BADA model). The better the expressions above predict the .
.
observed derivatives h and r , the more accurately the trajectory resulting from integration of such derivatives will fit the observed ones. Adopted optimization solution is least squares (LS) solution that minimizes the sum of square .
errors (SSE) of vertical speed h as defined in expression: i v SSE . = ∑ hi − (Ti − Di ) i ESFi h mi g i =1 n
2
(7)
where the referred errors are the differences .
between the observed (reference) values of h and the predicted ones. n is the total number of data samples through all the trajectories considered for the given aircraft type. To measure goodness of a specific model, the ½ RMS metric defined as RMS=(SSE/n) is used. This metric provides a measure of how well a specific model fits the reference data used to derive the model in terms of vertical speed.
A similar approach is taken for optimization of the fuel flow. In that case, the SSE is computed as n
. SSE . = ∑ m i + Fi m i =1
2
(8)
Current BADA model The current BADA model was first developed in the early 1990’s taking into consideration existing aircraft reference data availability, computing resources and target applications requirements. The main requirement at the time was to realistically simulate en-route aircraft behavior under nominal operating conditions. From user’s perspective ensuring large coverage of aircraft types was another important objective for BADA to meet. Aircraft types coverage The latest version of BADA provides 99.14% coverage of the European fleet mix [4]. 88 aircraft types are developed from original aircraft data and are referred to as original models. Additional 204 aircraft types may be simulated as being equivalent to an original model. Model structure Current BADA defines models for aircraft forces (aerodynamic and propulsive), limitations and operations for en-route and Terminal Maneuvering Area (TMA) operations.
Drag for aircraft clean and non-clean configurations, thrust and fuel flow models for maximum climb, maximum cruise and descent thrust levels for three engine types (jet, turboprop and piston) are provided. Governed by TEM, operations model supports simulation of flight regimes where any two of three variables of thrust, speed or vertical speed can be controlled, while third one is calculated. Standard airline procedure models for climb, cruise and descent, parameterized by BADA, are also provided. Limitations model defines maximum speeds and altitudes, minimum speeds at different aircraft configurations including low speed buffeting. Further details on the current BADA model are provided in reference document [4].
Model identification and accuracy levels Aircraft profile data used for identification of the current BADA aircraft models (3.x family) come from AOMs or aircraft performance software data sources that are available at Eurocontrol. The type and quality of the available reference data vary in function of aircraft type. In principle, available data with the best quality is used to identify the aircraft model coefficients. The existing aircraft models are regularly updated, provided that the better quality data becomes available.
The latest version of BADA (3.6) provides native model instances for 88 aircraft types. 56 of them are generated using AOM type of reference data and represent 27% of the European air traffic. Remaining 32 aircraft models are based on the aircraft performance engineering programs data and account for 55% of the European traffic. The coefficient optimization tools, appropriate fitting schemes and modeling techniques have been developed to identify the aircraft model coefficients from different types of the reference data. The objective of the model identification is to obtain as small as possible value of RMS error for vertical speed and fuel consumption. To ensure that obtained coefficients robustly represent aircraft behavior over normal operation conditions, a variety of flight profiles that cover operations of aircraft for different speeds, aircraft masses and ISA conditions are required. These can be specified as: • •
•
descent profiles at ISA for nominal aircraft weight at low, nominal and high speed climb profiles at ISA and off ISA conditions (up to ISA +20) for min, nominal and max aircraft weight at low, nominal and high speed cruise fuel flow data at ISA conditions for min, nominal and max aircraft weight at nominal speed
The available aircraft performance reference data does not always cater for this requirement of aircraft flight envelope coverage. In this case an aircraft model can be identified, but its fidelity can only be assessed and guaranteed for the range of reference data conditions.
Most of the aircraft types currently modeled in BADA demonstrate mean RMS error in vertical speed lower than 100 feet per minute [fpm], over previously specified normal operation conditions. This corresponds to mean error of vertical speed lower then 5% for operational range of flight envelope under assumption that 2000 fpm is an average vertical speed value. Fuel consumption is modeled with mean error lower than 5% for the same conditions. An example of vertical speed RMS error in fpm for 13 climb (CL) profiles of a wide body aircraft in BADA 3.6 is given in table 1. Table 1. Mean RMS Errors in ROC over 13 Climb Profiles CL RMS [fpm]
1
2
3
4
5
6
7
8
9
10
11
12
13
74
52
29
98
69
47
72
63
77
94
86
71
83
Model limitations The advanced model optimization tools and newly available high quality reference data have been used to study ability of the current BADA model to capture aircraft performances over the whole flight envelope and to identify levels of accuracy that are achievable.
For this reason, two model instances (two sets of coefficients) based on the current BADA model structure and algorithms were developed for a number of aircraft models using same type and source of the reference data, but covering different range of operating conditions. First model instance was obtained from the reference data covering the normal operations range as specified before (in total 25 climb and descent flight profiles). The second model instance was developed by using 324 flight profiles covering complete aircraft speed and weight flight envelope from ISA+0 up to ISA+30 conditions. The accuracy of the model was analyzed in terms of mean RMS and absolute error in vertical speed. In the first case, current BADA model have demonstrated its ability to ensure good level of accuracy for range of aircraft normal operating conditions with RMS vertical speed error less then 100 fpm. In the latter case, when model tried to capture aircraft behavior over the whole flight envelope,
overall RMS vertical speed error increased to 300 fpm or more depending on aircraft type. A graphical example of absolute error in vertical speed under ISA+0 conditions for the two model instances is depicted in Figure 2 and 3 for B744 aircraft. Figure 2 shows absolute error over 18 profiles in climb and descent, covering aircraft normal operation envelope for the first model instance. .
Figure 2. Absolute Error of h [fpm] for 18 climb and descent profiles, ISA+0, Mach 0.48-0.88
As it can be seen from the central part of the graph, representing normal operating conditions, the absolute error is still around 100 fpm. However, the absolute error increases towards the edges of the flight envelope and becomes greater then 300 fpm. These results demonstrate the current BADA model’s ability to accurately model aircraft performances for normal operation conditions. Accuracy decrease at the marginal parts of the flight envelope indicates that similar level of accuracy can not be provided for a complete flight envelope, with current model structure and algorithms. This has been identified as one of the areas of the future model improvement and will be further discussed in the continuation of the paper.
Towards BADA 4.0 M
Time for Enhancement Since the time BADA was first developed, applications relying on APM have broadened significantly with new requirements to provide more and better features to support the increasing analysis and operational needs in ATM.
Hp
The absolute error in vertical speed for majority of the data points remains below 100 fpm. Figure 3 shows absolute error over 81 profiles in climb and descent, covering complete aircraft envelope for the second model instance. .
Figure 3. Absolute Error of h [fpm] for 195 Climb &Descent Profiles, ISA+0, Mach 0.26-0.9
The new requirements relate to accuracy of the modeled aircraft performances, the coverage of the complete aircraft operation envelope, the flight phases that can be represented, and the type of operations that an APM can support. To satisfy those requirements, today’s availability of aircraft manufacturer’s performance software facilitates the automated use of better quality reference data. On top of that, computing technology has evolved in such a way that currently available computing capabilities have outdated the previous need to over-rationalize the necessary computing resources.
M
Finally, Object Oriented Programming (OOP) and adoption of the Unified Modeling Language (UML) as the industry-wide modeling standard, now make easier to develop well-defined models and manage complexity. Hp
All the above circumstances now enable a different approach to aircraft performance modeling
and will be used to support enhancement of the BADA model.
model performance with respect to non-functional requirements (e.g. realism, accuracy, complexity, completeness, maintainability, etc).
Advanced Model Engineering for BADA
With the aim to achieve the best possible compromise among all the requirements that the future BADA model should satisfy, the following premises have been considered, based on state-ofthe-art knowledge and techniques:
Advanced Model Engineering for BADA (AMEBA) is an on-going research effort that supports definition of the next-generation BADA APM (referred to as BADA 4.0). The work is performed in cooperation with Boeing Research & Technology Europe by taking advantages of today’s aircraft performance reference data, computing capabilities and modeling techniques. Main objectives are to provide a realistic, accurate, and complete aircraft performance model: •
capable of supporting accurate computation of the geometric, kinematic and kinetic aspects of the aircraft behavior • applicable to a wide set of aircraft types, over the entire operation envelope, and in all phases of flight • with reasonable complexity, maintainability and computing requirements • susceptible of being identified from profile data The execution of AMEBA is divided in two phases. Phase 1, Improvement, has already been executed. Phase 2, Extension, is under its way. This paper presents details of the Phase 1, which focuses on improvement of model accuracy for en-route operations. For this purpose, new models for thrust, drag and fuel consumption have been developed and validated using aircraft manufacturer raw data.
Modeling Premises AMEBA focuses on ‘modeling’ activities in two senses: physical and systemic. Physical modeling involves the analysis of the underlying physical laws governing aircraft behavior and identification of the physical variables upon which aircraft performance is to be represented together with the selection of appropriate mathematical models to relate them. Systemic modeling refers to the way of organizing the APM architecture (structure and functions) as a system so functional requirements are met (e.g. provision of drag, thrust and fuel flow), together with an adequate balance of
i) An in-depth review of Flight Dynamics fundamentals underlying aircraft behavior has been conducted, under no simplifying assumptions other than those reasonable in the ATM context (e.g. no sideslip). This allows the model development to remain as generic as possible until further simplifications are introduced by applications for specific purposes. ii) Dimensional Analysis (DA) techniques [8] were applied to identify the right physical dependencies for the mathematical models created to represent the required aircraft performances (drag, thrust, fuel consumption, etc). Use of proper physical dependencies allows the elaboration of mathematical models that obtain higher accuracy with a smaller number of coefficients. Additionally, DA techniques allow isolating the model interfaces (which are based on the right physical dependencies) from the particular modeling and implementation decisions adopted (i.e. the specific mathematical models chosen to relate physical variables). This helps to discover the ‘natural’ architecture of the APM and minimizes the impact of future changes. Finally, through the application of DA techniques, the physical relationships are obtained in terms of dimensionless variables. This facilitates analysis and comparisons, prevents mistakes and, provided an adequate selection of dimensionless terms, allows discovering physical similarity relationships. iii) Use of Object Oriented Modeling (OOM) principles to identify the right roles and responsibilities of the different components encompassing the APM architecture. OOM principles effectively allow managing complexity and prevent taking inappropriate design decisions, thus leading to a more robust model organization.
δT=f(M,θT)
Methodology
for ∆TISA≥ TBP
(14)
The methodology followed during the AMEBA modeling effort using above described premises is now explained.
where θT= [1+M ( κ-1)/2]θ is the total temperature ratio; θ=T/T0 being the temperature ratio, T the local temperature and T0 the standard one at MSL.
Starting point After the review of aircraft performance fundamentals new dependencies for drag, thrust and fuel consumption models have been obtained through DA techniques.
iii) Fuel consumption is calculated through the new dimensionless fuel coefficient CF as:
2
i) Drag is calculated through the drag coefficient CD, expressed as a function of lift coefficient CL and Mach number1 M as D=½κp0SδM2CD
CD=f(CL,M)
(9)
where δ=p/p0 is the pressure ratio, p being the local pressure and p0 the standard pressure at mean sea level (MSL). ii) Thrust is calculated through the new dimensionless thrust coefficient CT as T/δ=WMTOW CT
(10)
where WMTOW is the maximum takeoff weight and, for idle thrust (IDLE) CT has the form CT=f(M,δ)
(11)
while for maximum takeoff (MTKOF), maximum climb (MCMB) and maximum cruise (MCRZ) engine ratings2, CT represents the so-called generalized thrust model, which depends on the Mach number and the throttle parameter δT CT=f(M,δT)
(12)
In those cases, separate laws for δT are provided for the off-ISA atmosphere conditions characterized by ∆TISA below and above the socalled blink point3 TBP: δT=f(M,δ) 1
for ∆TISA
